Solve for $x$ and $y$ using elimination. ${5x-4y = -10}$ ${-3x+y = -1}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $4$ ${5x-4y = -10}$ $-12x+4y = -4$ Add the top and bottom equations together. $-7x = -14$ $\dfrac{-7x}{{-7}} = \dfrac{-14}{{-7}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {5x-4y = -10}\thinspace$ to find $y$ ${5}{(2)}{ - 4y = -10}$ $10-4y = -10$ $10{-10} - 4y = -10{-10}$ $-4y = -20$ $\dfrac{-4y}{{-4}} = \dfrac{-20}{{-4}}$ ${y = 5}$ You can also plug ${x = 2}$ into $\thinspace {-3x+y = -1}\thinspace$ and get the same answer for $y$ : ${-3}{(2)}{ + y = -1}$ ${y = 5}$